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165 lines
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Copyright (C) 2021 Maxime Devos
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Copyright (C) 2024 Tomas Volf
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<title>Exactness (Guile Reference Manual)</title>
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<div class="subsubsection-level-extent" id="Exactness">
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<p>
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Next: <a href="Number-Syntax.html" accesskey="n" rel="next">Read Syntax for Numerical Data</a>, Previous: <a href="Complex-Numbers.html" accesskey="p" rel="prev">Complex Numbers</a>, Up: <a href="Numbers.html" accesskey="u" rel="up">Numerical data types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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<hr>
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<h4 class="subsubsection" id="Exact-and-Inexact-Numbers"><span>6.6.2.5 Exact and Inexact Numbers<a class="copiable-link" href="#Exact-and-Inexact-Numbers"> ¶</a></span></h4>
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<a class="index-entry-id" id="index-Exact-numbers"></a>
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<a class="index-entry-id" id="index-Inexact-numbers"></a>
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<a class="index-entry-id" id="index-exact_003f-2"></a>
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<a class="index-entry-id" id="index-inexact_003f-2"></a>
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<a class="index-entry-id" id="index-exact_002d_003einexact-2"></a>
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<a class="index-entry-id" id="index-inexact_002d_003eexact-2"></a>
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<p>R5RS requires that, with few exceptions, a calculation involving inexact
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numbers always produces an inexact result. To meet this requirement,
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Guile distinguishes between an exact integer value such as ‘<samp class="samp">5</samp>’ and
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the corresponding inexact integer value which, to the limited precision
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available, has no fractional part, and is printed as ‘<samp class="samp">5.0</samp>’. Guile
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will only convert the latter value to the former when forced to do so by
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an invocation of the <code class="code">inexact->exact</code> procedure.
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</p>
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<p>The only exception to the above requirement is when the values of the
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inexact numbers do not affect the result. For example <code class="code">(expt n 0)</code>
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is ‘<samp class="samp">1</samp>’ for any value of <code class="code">n</code>, therefore <code class="code">(expt 5.0 0)</code> is
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permitted to return an exact ‘<samp class="samp">1</samp>’.
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</p>
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<dl class="first-deffn">
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<dt class="deffn" id="index-exact_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">exact?</strong> <var class="def-var-arguments">z</var><a class="copiable-link" href="#index-exact_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-scm_005fexact_005fp"><span class="category-def">C Function: </span><span><strong class="def-name">scm_exact_p</strong> <var class="def-var-arguments">(z)</var><a class="copiable-link" href="#index-scm_005fexact_005fp"> ¶</a></span></dt>
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<dd><p>Return <code class="code">#t</code> if the number <var class="var">z</var> is exact, <code class="code">#f</code>
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otherwise.
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</p>
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<div class="example lisp">
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<pre class="lisp-preformatted">(exact? 2)
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⇒ #t
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(exact? 0.5)
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⇒ #f
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(exact? (/ 2))
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⇒ #t
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</pre></div>
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</dd></dl>
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<dl class="first-deftypefn">
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<dt class="deftypefn" id="index-scm_005fis_005fexact"><span class="category-def">C Function: </span><span><code class="def-type">int</code> <strong class="def-name">scm_is_exact</strong> <code class="def-code-arguments">(SCM z)</code><a class="copiable-link" href="#index-scm_005fis_005fexact"> ¶</a></span></dt>
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<dd><p>Return a <code class="code">1</code> if the number <var class="var">z</var> is exact, and <code class="code">0</code>
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otherwise. This is equivalent to <code class="code">scm_is_true (scm_exact_p (z))</code>.
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</p>
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<p>An alternate approach to testing the exactness of a number is to
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use <code class="code">scm_is_signed_integer</code> or <code class="code">scm_is_unsigned_integer</code>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-inexact_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">inexact?</strong> <var class="def-var-arguments">z</var><a class="copiable-link" href="#index-inexact_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-scm_005finexact_005fp"><span class="category-def">C Function: </span><span><strong class="def-name">scm_inexact_p</strong> <var class="def-var-arguments">(z)</var><a class="copiable-link" href="#index-scm_005finexact_005fp"> ¶</a></span></dt>
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<dd><p>Return <code class="code">#t</code> if the number <var class="var">z</var> is inexact, <code class="code">#f</code>
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else.
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</p></dd></dl>
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<dl class="first-deftypefn">
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<dt class="deftypefn" id="index-scm_005fis_005finexact"><span class="category-def">C Function: </span><span><code class="def-type">int</code> <strong class="def-name">scm_is_inexact</strong> <code class="def-code-arguments">(SCM z)</code><a class="copiable-link" href="#index-scm_005fis_005finexact"> ¶</a></span></dt>
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<dd><p>Return a <code class="code">1</code> if the number <var class="var">z</var> is inexact, and <code class="code">0</code>
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otherwise. This is equivalent to <code class="code">scm_is_true (scm_inexact_p (z))</code>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-inexact_002d_003eexact"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">inexact->exact</strong> <var class="def-var-arguments">z</var><a class="copiable-link" href="#index-inexact_002d_003eexact"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-scm_005finexact_005fto_005fexact"><span class="category-def">C Function: </span><span><strong class="def-name">scm_inexact_to_exact</strong> <var class="def-var-arguments">(z)</var><a class="copiable-link" href="#index-scm_005finexact_005fto_005fexact"> ¶</a></span></dt>
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<dd><p>Return an exact number that is numerically closest to <var class="var">z</var>, when
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there is one. For inexact rationals, Guile returns the exact rational
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that is numerically equal to the inexact rational. Inexact complex
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numbers with a non-zero imaginary part can not be made exact.
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</p>
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<div class="example lisp">
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<pre class="lisp-preformatted">(inexact->exact 0.5)
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⇒ 1/2
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</pre></div>
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<p>The following happens because 12/10 is not exactly representable as a
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<code class="code">double</code> (on most platforms). However, when reading a decimal
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number that has been marked exact with the “#e” prefix, Guile is
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able to represent it correctly.
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</p>
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<div class="example lisp">
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<pre class="lisp-preformatted">(inexact->exact 1.2)
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⇒ 5404319552844595/4503599627370496
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#e1.2
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⇒ 6/5
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</pre></div>
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</dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-exact_002d_003einexact"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">exact->inexact</strong> <var class="def-var-arguments">z</var><a class="copiable-link" href="#index-exact_002d_003einexact"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-scm_005fexact_005fto_005finexact"><span class="category-def">C Function: </span><span><strong class="def-name">scm_exact_to_inexact</strong> <var class="def-var-arguments">(z)</var><a class="copiable-link" href="#index-scm_005fexact_005fto_005finexact"> ¶</a></span></dt>
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<dd><p>Convert the number <var class="var">z</var> to its inexact representation.
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</p></dd></dl>
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</div>
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<hr>
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<div class="nav-panel">
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<p>
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Next: <a href="Number-Syntax.html">Read Syntax for Numerical Data</a>, Previous: <a href="Complex-Numbers.html">Complex Numbers</a>, Up: <a href="Numbers.html">Numerical data types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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